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 No trigonometry, no algebra (Posted on 2005-12-23)
Look at the drawing below, where AB = BC = CD = DT = h, and TD perpendicular to AD:
```
o T
|
| (h)
|
|
+----------+----------+----------o
A    (h)   B    (h)   C    (h)   D```
The line AT makes an angle x with AD; the line BT makes an angle y with BD; the line CT makes an angle z with CD.

Using only geometry, prove that (angle x) + (angle y) = (angle z).

 See The Solution Submitted by pcbouhid Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 With Trig. Identity | Comment 5 of 10 |
` `
`                                      1     1                                     --- + ---                tan(x) + tan(y)        3     2  tan(x+y) = ------------------- = ------------- = 1 = tan(z)              1 - tan(x)*tan(y)          1   1                                    1 - ---x---                                         3   2`
`Therefore, z = x+y`

 Posted by Bractals on 2005-12-24 03:41:34

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